### GaAs/AlAs Quantum Well

#### Band Structure Calculation

In this example a 250nm wide $GaAs$ structure was embedded between two $AlAs$ regions. The growth direction was in the $100$ axis, and it was grown in theoretically on $AlAs$.

The built up strain in the structure due the lattice mismatch is shown on the following figure:

Strain-profile in a GaAs/AlAs structure

The band-edges are calculated with 6 band k.p method for valence bands, and uncoupled conduction bands. The result can be seen on the following figure:

Bandstructure in a of GaAs/alAs structure

#### Carrier Density

The Poisson equation was solved, with the condition that the sum charge in the device should be 0. It add an additional electrostatic potential term to the band structure. The Resulted potential shifted band structure can be seen on the following figure, when the Fermi level is at $0$ eV.

Bandstructure in a of GaAs/alAs structure shifted with the electrostatic potential